# Memorization in Language Models through the Lens of Intrinsic Dimension

arXiv: https://arxiv.org/abs/2506.09591 · HTML: https://mlsanity.com/paper/2506.09591/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 37 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 24 of 24)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [The Secret Sharer: Evaluating and Testing Unintended Memorization in Neural Networks](https://mlsanity.com/paper/1802.08232/) (2018)
- [Deduplicating Training Data Makes Language Models Better](https://mlsanity.com/paper/2107.06499/) (2021)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Scalable Extraction of Training Data from (Production) Language Models](https://mlsanity.com/paper/2311.17035/) (2023)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Deduplicating Training Data Mitigates Privacy Risks in Language Models](https://mlsanity.com/paper/2202.06539/) (2022)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Are Large Pre-Trained Language Models Leaking Your Personal Information?](https://mlsanity.com/paper/2205.12628/) (2022)
- [Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts](https://mlsanity.com/paper/2306.04723/) (2023)
- [When is Memorization of Irrelevant Training Data Necessary for High-Accuracy Learning?](https://mlsanity.com/paper/2012.06421/) (2020)
- [Preventing Verbatim Memorization in Language Models Gives a False Sense of Privacy](https://mlsanity.com/paper/2210.17546/) (2022)
- [Generalization v.s. Memorization: Tracing Language Models' Capabilities Back to Pretraining Data](https://mlsanity.com/paper/2407.14985/) (2024)
- [Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks](https://mlsanity.com/paper/2111.13171/) (2021)
- [Persistent Homology and the Upper Box Dimension](https://mlsanity.com/paper/1802.00533/) (2018)

## Built on by (most cited first, 3 of 3)

- [The Trigger in the Haystack: Extracting and Reconstructing LLM Backdoor Triggers](https://mlsanity.com/paper/2602.03085/) (2026)
- [Unveiling Intrinsic Dimension of Texts: from Academic Abstract to Creative Story](https://mlsanity.com/paper/2511.15210/) (2025)
- [A Comparative Analysis of LLM Memorization at Statistical and Internal Levels: Cross-Model Commonalities and Model-Specific Signatures](https://mlsanity.com/paper/2603.21658/) (2026)

## Abstract (arXiv)

Language Models (LMs) are prone to memorizing parts of their data during training and unintentionally emitting them at generation time, raising concerns about privacy leakage and disclosure of intellectual property. While previous research has identified properties such as context length, parameter size, and duplication frequency, as key drivers of unintended memorization, little is known about how the latent structure modulates this rate of memorization. We investigate the role of Intrinsic Dimension (ID), a geometric proxy for the structural complexity of a sequence in latent space, in modulating memorization. Our findings suggest that ID acts as a suppressive signal for memorization: compared to low-ID sequences, high-ID sequences are less likely to be memorized, particularly in overparameterized models and under sparse exposure. These findings highlight the interaction between scale, exposure, and complexity in shaping memorization.